List of commands

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

A

Abs -- absolute value of a number
Adjoint -- adjoint matrix
Alias -- define aliases for package names
Alias In -- temporarily override global aliases
Aliases -- list of global aliases
Append -- append an object to an existing list
Ascii -- convert between characters and ascii code

B

Bin -- binomial coefficient
BinExp, EvalBinExp -- binomial expansion
Block -- group several commands into a single command
BlockMatrix -- create a block matrix
Break -- break out of a loop
BringIn -- bring in objects from another ring

C

Call -- apply a function to given arguments
Cast -- type conversion
Catch -- catch an error
CFApprox, CFApproximants, ContFrac -- continued fractions
Characteristic -- the characteristic of a ring
Ciao -- quit CoCoA
Clear -- clear the working memory or a ring-bound memory
Close -- close a device
CocoaLimits -- limits on exponents and ring characteristics
CocoaPackagePath -- returns the path to the CoCoA packages
Coefficients -- list of coefficients of a polynomial or vector
CoeffOfTerm -- coefficient of a term of a polynomial or vector
Colon, :, HColon -- ideal or module quotient
ColumnVectors -- the list of column vectors of a matrix
Comp -- the N-th component of a list
Comps -- list of components of a vector
Concat, ConcatLists -- concatenate lists or lists of lists, respectively
Cond -- conditional expression
Contrib -- list of contributors to CoCoA
Count -- count the objects in a list
CurrentRing -- the current ring

D

Dashes -- returns string of dashes
Date -- the date
DecimalStr -- convert rational number to decimal string
Define -- define a function
Defined -- check if an expression has been defined
Deg -- the degree of a polynomial or vector
DegLexMat, DegRevLexMat, LexMat, XelMat -- matrices for std. term-orderings
Delete -- delete variables from the working memory
DensePoly -- the sum of all power-products of a given degree
Der -- the derivative of a rational function
Describe -- information about an expression
Destroy -- delete rings
Det -- the determinant of a matrix
Diff -- returns the difference between two lists
Dim -- the dimension of a ring or quotient object
Discriminant -- the discriminant of a polynomial
Distrib -- the distribution of objects in a list
Div, Mod -- quotient and remainder for integers
DivAlg -- division algorithm

E

E_ -- canonical vector
Elim -- eliminate variables
EqSet -- checks if the set of elements in two lists are equal
Equals -- returns a string of equal signs
EquiIsoDec -- equidimensional isoradical decomposition
Error -- return an error message
Eval -- substitute numbers or polynomials for indeterminates
EvalHilbertFn -- evaluate the Hilbert function

F

Fact -- factorial function
Factor -- factor a polynomial
Fields -- list the fields of a record
First -- the first N elements of a list
FirstNonZero, FirstNonZeroPos -- the first non-zero entry in a vector
Flatten -- flatten a list
FloatApprox -- approx. of rational number of the form M*10^E
FloatStr, MantissaAndExponent -- convert rational number to a float string
For -- loop command
Foreach -- loop command
Format -- convert object to formatted string
Fraction -- returns the quotient of its arguments
Function -- return a function
Functions -- list the functions of a package

G

GB.Complete -- Complete an interactive Groebner-type calculation
GB.GetBettiMatrix -- returns the Betti matrix computed so far
GB.GetNthSyz -- returns the part of the Nth syzygy module computed so far
GB.GetNthSyzShifts -- shifts of the Nth syzygy module computed so far
GB.GetRes -- returns the resolution computed so far
GB.GetResLen -- returns the length of the resolution computed so far
GB.ResReport -- status of an interactive resolution calculation
GB.Start_GBasis -- start interactive Groebner basis computation
GB.Start_MinGens -- start interactive minimal generator calculation
GB.Start_MinSyzMinGens -- start interactive calc., min. syzs. of min. gens.
GB.Start_Res -- start interactive resolution computation
GB.start_Syz -- start interactive syzygy computation
GB.start_SyzMinGens -- start interactive calc. of syzygies of min. gens.
GB.Stats -- status of an interactive Groebner-type calculation
GB.Step, GB.Steps -- take steps in an interactive Groebner-type calculation
GBasis -- calculate a Groebner basis
GBM, HGBM -- intersection of ideals for zero-dimensional schemes
GCD, LCM -- greatest common divisor, least common multiple
GenericPoints -- random projective points
GenRepr -- representation in terms of generators
Gens -- list of generators of an ideal
Get -- read characters from a device
GetErrMesg -- returns the message associated with an error
Gin -- generic initial ideal
GlobalMemory -- contents of global memory

H

H.Browse -- browse the online help system
H.Commands -- list commands according to type
H.Man -- search online help system (see "?, Man")
H.OutCommands -- print command descriptions to a file
H.OutManual -- print the online manual to a file
H.SetMore, H.UnSetMore -- more-device for online help
H.Syntax -- display the syntax of a command
H.Tips -- quick tips for using online help
H.Toc -- display the Table Of Contents of the online manual
H.Tutorial -- run the CoCoA tutorial
Head -- the first element of a list
Help -- extend online help for user-defined functions
Hilbert -- the Hilbert function
HilbertBasis -- Hilbert basis for a monoid
HilbertPoly -- the Hilbert polynomial
HIntersection, HIntersectionList -- intersection of ideals
Homogenized -- homogenize with respect to an indeterminate
HVector -- the h-vector of a ring or quotient object

I

Ideal -- convert an expression into an ideal
IdealAndSeparatorsOfPoints -- ideal and separators for affine points
IdealAndSeparatorsOfProjectivePoints -- ideal and separators for points
IdealOfPoints -- ideal of a set of affine points
IdealOfProjectivePoints -- ideal of a set of projective points
Identity -- the identity matrix
If -- conditional statement
ILogBase -- integer part of the logarithm
Image -- ring homomorphism
In -- create a list satisfying given conditions
Indet -- individual indeterminates
IndetInd -- the index of an indeterminate
IndetIndex -- index of an indeterminate
IndetName -- the name of an indeterminate
Indets -- list of current indeterminates
Insert, Remove -- insert or remove an object in a list
Interpolate -- interpolating polynomial
Interreduce, Interreduced -- interreduce a list of polynomials or vectors
Intersection, IntersectionList -- intersect lists, ideals, or modules
Inverse -- multiplicative inverse
IO.SprintTrunc -- convert to a string and truncate
Iroot -- integer part of r-th root of an integer
IsEven, IsOdd -- test whether an integer is even or odd
IsHomog -- test whether given polynomials are homogeneous
IsIn -- check if one object is contained in another
IsNumber -- checks if the argument is a number
IsPosTo, IsToPos -- checks the module term-ordering of a ring
IsPrime -- prime integer test
Isqrt -- computes the (truncated) square root of an integer
IsStable, IsStronglyStable, IsLexSegment -- checks if an ideal is stable (resp. strongly stable or a lex-segment)
IsSubset -- checks if the elements of one list are a subset of another
IsTerm -- checks if the argument is a term
IsZero -- test whether an object is zero

J

Jacobian -- the Jacobian of a list of polynomials

K

L

Last -- the last N elements of a list
Latex -- LaTeX formatting
LC -- the leading coefficient of a polynomial or vector
Len -- the length of an object
LinKer -- find the kernel of a matrix
LinSol -- find a solution to a linear system
List -- convert an expression into a list
LM -- the leading monomial of a polynomial or vector
Log -- the list of exponents of the leading term of a polynomial
LogToTerm -- returns a monomial (power-product) with given exponents
LPos -- the position of the leading power-product in a vector
LPP -- the leading power-product of a polynomial or vector
LT -- the leading term of an object

M

MapDown -- convert a constant polynomial to a number
Mat -- convert an expression into a matrix
Max, Min -- a maximum or minimum element of a sequence or list
MDeg -- multi-degree of an polynomial
Memory -- contents of local memory or ring-bound memory
MinGens -- list minimal generators
Minimalize, Minimalized -- remove redundant generators
Minors -- list of minor determinants of a matrix
MinSyzMinGens -- minimal generators of syzygies of minimal generators
Mod2Rat -- reconstructing rationals from modular integers
Module -- convert an expression into a module
Monic -- divide polynomials by their leading coefficients
Monomials -- the list of monomials of a polynomial or vector
MonsInIdeal -- ideal generated by the monomials in an ideal
More -- print a string, N lines at a time
Multiplicity -- the multiplicity (degree) of a ring or quotient object

N

NewId -- create a new identifier
NewList -- create a new list
NewMat -- create a new matrix
NewVector -- create a new vector
NextPrime -- find the next largest prime number
NF -- normal form
NFsAreZero -- test if normal forms are zero
NonZero -- remove zeroes from a list
Not, And, Or -- boolean operators
NR -- normal reduction
Num, Den -- numerator, denominator
NumComps -- the number of components of a vector
NumIndets -- number of indeterminates

O

OpenIFile, OpenOFile -- open input or output file
OpenIString, OpenOString -- open input or output string
OpenLog, CloseLog -- open or close a log of a CoCoA session
Option -- status of a panel option
Ord -- matrix defining a term-ordering

P

Packages -- list of loaded packages
Panel -- print status of a panel's options
Panels -- list of CoCoA panels
Partitions -- partitions of an integer
Permutations -- returns all permutations of the entries of a list
Pfaffian -- the Pfaffian of a skew-symmetric matrix
PkgName -- returns the name of a package
Poincare, HilbertSeries -- the Poincare series
Poly -- convert an expression into a polynomial
PrimaryDecomposition -- primary decomposition of an ideal
Print On -- print to an output device
Print, PrintLn -- print the value of an expression
Product, Sum -- the product or sum of the elements of a list

Q

Quit -- quit CoCoA
QuotientBasis -- vector space basis for zero-dimensional quotient rings
QZP, ZPQ -- change field for polynomials and ideals

R

Radical -- radical of an ideal
RadicalOfUnmixed -- radical of an unmixed ideal
Rand -- random integer
Randomize, Randomized -- randomize the coefficients of a given polynomial
Rank -- rank of a module
RealRootRefine -- refine a root of a univariate polynomial over Q
RealRoots -- computes a root of a univariate polynomial over Q
Record -- create a record
ReducedGBasis -- compute a reduced Groebner basis
Repeat -- loop command
Res -- free resolution
Reset -- reset panels and random number seed to defaults
ResetPanels -- reset panels to their default values
Resultant -- the resultant of two polynomials
Return -- exit from a structured command
Reverse, Reversed -- reverse a list
Ring -- returns the ring with a given name
RingEnv -- name of the current ring
RingEnvs -- names of all defined rings
RootBound -- bound on roots of a polynomial over Q

S

Saturation, HSaturation -- saturation of ideals
ScalarProduct -- scalar product
Seed -- seed for Rand
SeparatorsOfPoints -- separators for affine points
SeparatorsOfProjectivePoints -- separators for projective points
Set -- remove duplicates from a list
Set, Unset -- set and unset panel options
Shape -- extended list of types involved in an expression
Size -- the amount of memory used by an object
Skip -- does nothing
Sort, Sorted -- sort a list
SortBy, SortedBy -- sort a list
Source, << -- read commands from a file or device
Spaces -- return a string of spaces
Sprint -- convert to a string
StarPrint -- print polynomial with *'s for multiplications
Starting -- list functions starting with a given string
Submat -- submatrix
Subsets -- returns all sublists of a list
Subst -- substitute values for indeterminates
Support -- the list of terms of a polynomial or vector
Sylvester -- the Sylvester matrix of two polynomials
Syz -- syzygy modules
SyzMinGens -- syzygy module for a set of minimal generators
SyzOfGens -- syzygy module for a given set of generators

T

Tag -- returns the tag string of an object
Tagged, Untagged, @ -- tag or untag an object for pretty printing
Tail -- remove the first element of a list
TensorMat -- returns the tensor product of two matrices
Toric -- saturate toric ideals
Toric.CheckInput -- check input to Toric
Transposed -- the transposition of a matrix
Tuples -- N-tuples
Type -- the data type of an expression
TypeOfCoeffs -- type of the coefficients of the current ring
Types -- lists all data types

U

Use -- command for making a ring active
Using -- perform commands in non-active ring

V

Var -- function calls by reference, other complex referencing
Vector -- create a vector

W

WeightsList -- first row of the weights matrix
WeightsMatrix -- matrix of generalized weights for indeterminates
While -- loop command
WithoutNth -- removes the N-th component from a list
WLog -- weighted list of exponents

X

Y

Z